arXiv subjects
Publications and source records attributed to Hongwei Liu.
In this paper, the homogeneous weights of matrix product codes over finite principal ideal rings are studied and a lower bound for the minimum homogeneous weights of such matrix product codes is obtained.
When a material is subjected to an applied stress, the material will experience recoverable elastic deformation followed by permanent plastic deformation at the point when the applied stress exceeds the yield stress of the material. Microscopically, the onset of the plasticity usually indicates the activation of dislocation motion, which is considered to be the primary mechanism of plastic deformation. Once plastic deformation is initiated, further elastic deformation is negligible owing to the limited increase in the flow stress caused by work hardening. Here we present experimental evidence and quantitative analysis of simultaneous development of significant elastic deformation and dislocation-based plastic deformation in single crystal GaAs nanowires (NWs) under bending deformation up to a total strain of ~ 6%. The observation is in sharp contrast to the previous notions regarding the deformation modes. Most of the plastic deformation recovers spontaneously when the external stress is released, and therefore resembles an elastic deformation process.
An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length $\ell^tp^s$ are characterized, where $p$ is the characteristic of the finite field and $\ell$ is a prime different from $p$.
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a very sharp threshold point for the density of the linear codes whose relative distance is greater than a given positive number. For arbitrary random codes, similar settings and results are exhibited; in particular, the very sharp threshold point for the density of the codes whose relative distance is greater than a given positive number is located at half the asymptotic Gilbert-Varshamov bound.
We study codes with a single check element derived from group rings, namely, checkable codes. The notion of a code-checkable group ring is introduced. Necessary and sufficient conditions for a group ring to be code-checkable are given in the case where the group is a finite abelian group and the ring is a finite field. This characterization leads to many good examples, among which two checkable codes and two shortened codes have minimum distance better than the lower bound given in Grassl's online table. Furthermore, when a group ring is code-checkable, it is shown that every code in such a group ring admits a generator, and that its dual is also generated by an element which may be deduced directly from a check element of the original code. These are analogous to the generator and parity-check polynomials of cyclic codes. In addition, the structures of reversible and complementary dual checkable codes are established as generalizations of reversible and complementary dual cyclic codes.